If you light the yahrzeit candle before it's time to light the Hanukkah-menorah, you may light the yahrzeit candle first.

Otherwise, once it's past sunset, you should wait until about 20 minutes after sunset, light the Hanukkah-menorah, and afterwards light the yahrzeit candle.

Yahrzeit is a commemoration of the death of a Jew by a mourner (the child, sibling, spouse or parent of the deceased).

The date of the Yahrzeit, which is calculated according to the Hebrew calendar, is the anniversary of the death, not the burial.

The anniversary of the death of a loved one is naturally a solemn day, and Judaism helps the mourner experience this pain and and also honors the memory of the deceased via Yahrzeit rituals.

Yes.

Yahrzeit (literally "Time of the Year" and connotatively "anniversary") is the anniversary of the death, not the burial. So the first yahrzeit would be observed on the first anniversary of the date of death. However, some authorities rule that if the burial takes place more than three days after death (the day of death being considered day one) that the first yahrzeit take place on the day of burial.

Yes, I think so.